Mindful of its declining appetite for projecting power in the Middle East, the U.S. is relying on more activist partners in the region such Qatar, Saudi Arabia and Turkey to arm the Syrian rebellion. But Tuesday’s visit to Gaza by Qatar’s Sheikh Hamad bin Khalifa al-Thani — to the delight of the territory’s Hamas rulers and Egypt’s Muslim Brotherhood, while Israel and Fatah fumed — was a reminder that U.S. allies in the region often pursue goals quite different from those of Washington, despite many shared objectives and common enemies. And the relative decline of U.S. influence in the Middle East has seen some of those independently-minded allies grow more assertive in pressing their agendas.

In Monday’s presidential campaign foreign policy debate, Gov. Mitt Romney rejected U.S. military intervention in Syria, noting instead that “The Saudis and the Qataris and the Turks are … willing to work with us. We need to have a very effective leadership effort in Syria, making sure that the insurgents there are armed, and that the insurgents that become armed are people who will be the responsible parties.” President Obama also talked up cooperation with regional allies, but warned that “we have to [make] absolutely certain that we know who we are helping; that we’re not putting arms in the hands of folks who eventually could turn them against us or allies in the region.”

But the Emir’s visit to Gaza makes clear that Qatar, the tiny Emirate whose massive natural gas reserves give it the world’s highest per capita income as well as geopolitical punching power way above its weight, has sharply different ideas from Washington’s about just who the “responsible parties” will be in a changing Middle East. Hamas, after all, is formally shunned by the U.S. and European powers as a terrorist organization, and Washington has shown little enthusiasm for efforts by Arab governments, including Qatar, to promote reconciliation between the Islamists and the Fatah movement of President Mahmoud Abbas. Abbas was reportedly furious at the Qatari leader’s decision to become the first foreign head of state to visit the Hamas-controlled Gaza, effectively blessing the Islamist’ rule there. The Emir’s purpose was to inaugurate Qatar’s $400 billion investment in rebuilding infrastructure smashed in repeated confrontations with Israel — a massive stimulus to an economy choked off by a five-year siege imposed by Israel with Egyptian compliance.

Sheik Hamad seemed unmoved by Abbas’ ire or Washington’s discomfort, his effort to rehabilitate Gaza and coax Hamas into the Arab mainstream prompted by the malign neglect of Gaza by all parties to the now moribund peace process. It’s also a reflection of the political paralysis of Fatah after a decade of passively waiting in vain for the U.S. to restart a credible peace process. And, there’s thinly disguised geopolitical agenda, too: driving a wedge between Iran and Hamas, and drawing the movement back into the moderate Islamist mainstream.

It’s also worth noting, however, that the mass rally planned as the centerpiece of Sheikh Hamad’s visit was abruptly canceled at the last minute, when the soccer-stadium venue was just one-fifth full and it became clear that the Gaza public wasn’t exactly rushing to the event — Gaza Palestinians are just as disdainful of their Hamas rulers as West Bank Palestinians are of their Fatah rulers, as was demonstrated in the low turnout at municipal election last weekend boycotted by Hamas — and even then, the official Fatah candidates lost six of the 11 main seats. The Qatari leader did address a smaller crowd at a local university, and urged reconciliation between Hamas and Fatah.”Why are you staying divided?” he said. “There are no peace negotiations, and there is no clear strategy of resistance and liberation. Why shouldn’t brothers sit together and reconcile?”

Washington responded cautiously to the visit, preferring — at least publicly — to take at face value Qatar’s insistence that the visit had an entirely “humanitarian” purpose. “We share Qatar’s deep concern for the welfare of the Palestinian people including those residing in Gaza,” said State Department spokesperson Victoria Nuland on Tuesday. We remain concerned about Hamas’ destabilizing role in Gaza and the region, and we urge all parties in the region to play a constructive role in bringing the Palestinians and Israelis back to the negotiating table.”

Promoting peace is exactly what the Qataris would say they’re doing in Gaza, and in pressing for Palestinian reconciliation. The idea of a more assertive Palestinian polity that includes Hamas in a prominent role won’t appeal to either Washington or Israel, of course, nor to Abbas who has long claimed a monopoly on representing the Palestinians regardless of the verdict of his electorate. But Palestinian society has grown largely indifferent to Abbas’ diplomatic wanderings, and re-engaging them in the search for a national strategy may be critical to the prospects of winning legitimacy for any future peace deal. And a Hamas lawmaker involved in the visit, speaking anonymously, told the AP that “the Qatari leader urged Hamas to reconcile with Abbas’ forces and do everything possible to avoid violence with Israel.”

Even as it embraces Hamas, Qatar remains one of that rare species of Arab states that openly maintains relations with Israel. It also hosts the forward operating headquarters of CENTCOM, the U.S. military command that covers the Middle East. But the Emirate is not simply trying to hedge its bets; its interventions in support of the Arab rebellions of the past two years reflect a clear-eyed strategy of boosting its own influence via mainstream Islamist political forces, chiefly the Muslim Brotherhood and its affiliates (of which Hamas is essentially the progeny). Qatar’s influence grows not only at the expense of Western-backed secularists, but also of the extremist salafi current, most of whose external support allegedly comes from Saudi Arabia — and, most importantly in the Gaza instance, at the expense of influence by Iran.

Qatar may be on cordial terms with Iran, but the two nations are strategic competitors — not least because they share the South Pars natural gas field which is the world’s largest. Qatar aligns itself with a moderate Sunni Islamist politics exemplified by the Muslim Brotherhood, which serves as a de facto bulwark against Iranian influence in Arab countries. Iran’s influence had grown during the Bush Administration era, when dictators such as Egypt’s President Hosni Mubarak were perceived by their public as supine in the face of the invasion of Iraq, and U.S. backing for Israel’s wars in Gaza and Lebanon. But the Arab rebellions that swept away Mubarak and challenged other U.S.-aligned strongmen was bad news for Iran, precisely because it offered an indigenous alternative that both expressed democratic aspirations, and challenged U.S. policy in the region. Hamas had been something of an exception for a Muslim Brotherhood organization, having found itself largely dependent on Iran and Syria after the siege of Gaza took effect in 2007. Qatar’s mission, in part, has been to woo Hamas back into the Arab fold and wean it off support from Tehran — the Emir’s Gaza visit was widely interpreted as in part a reward for Hamas breaking ties with the Assad regime in Syria last, its former host, a move that angered Iran.

Although the Arab rebellion weakened the Iran-Syria “resistance camp” to which Hamas had been aligned, it also brought Hamas’ parent organization, Egypt’s Muslim Brotherhood, to power in Cairo, as well as empowering like-minded mainstream Islamist parties across the region. Turkey’s moderate Islamist AK Party rulers have also assiduously courted Hamas over the past four years — the organization’s leader, Khaled Meshal, was welcomed with rock-star adulation when he attended the AKP’s annual convention last month.

And, of course, Qatar has been at the forefront of promoting the Arab rebellion, through deploying soft-power and hard: Its international TV news station, al-Jazeera, covered the uprisings (except, perhaps, for Bahrain’s) with a courage and enthusiasm that helped turned protests that began in Tunisia at the end of 2010 into a region-wide seismic political event.

When Libya’s rebellion turned violent, Qatar took the lead in winning Arab League support a NATO air campaign against Gaddafi, sending its own fighter jets — and then, perhaps more importantly, covertly deploying hundreds of its own special forces on the ground to coordinate the rebel assault that captured Tripoli. In Syria, too, the Emir has said Arabs have a “military duty” to intervene, and has pressed for international action, while reportedly taking a lead in arming rebel forces.

But in all of its interventions, Qatar is discerning, throwing its resources behind its own preferred interlocutors — rival Libyan factions complained that Doha’s support was going principally to the Islamist militia of Abdulaziz Belhadj, while it has reportedly given considerable financial and logistical support to Tunisia’s Ennahda party and Egypt’s Muslim Brotherhood, prompting complaints of meddling. In Syria, too, Qatar is believed to be favoring the Muslim Brotherhood in the support it directs to the rebellion.

By betting on the Muslim Brotherhood as the vehicle for its influence throughout the region, Qatar may also be creating an insurance policy for itself, domestically, by having the region’s most powerful political party on board. But it’s not simply defensive; Doha has moved aggressively to take advantage of the region’s political flux to promote its Islamist allies. That’s been good news for Hamas, although the opportunities it has opened up for the Palestinian movement are on the more moderate side of the Islamist street — a trend that Qatar’s investment in Gaza is intended to incentivize. But the “moderate” may mean something quite different in a rapidly democratizing Arab world from what the U.S. would like to see. Then again, no democratically accountable Arab leadership would likely have endorsed the U.S. invasion of Iraq, or U.S. policy towards the Israeli-Palestinian and towards Iran.

Sheikh Hamad’s Gaza visit is a symptom of the Middle East’s political order slipping further beyond U.S. control, to a more independent — but not necessarily hostile — position. Indeed, part of Qatar’s strategy appears to be encouraging restraint on the part of Hamas, and insulating it from Iranian influence. Sure, the U.S. won’t like it, but from Qatar’s point of view, Washington’s policy has been dysfunctional and unsustainable.

The spectacle of a U.S. ally to which arming the Syrian opposition is being outsourced embracing a Palestinian movement branded as a terrorist organization by Washington is a sobering reminder that when the Middle East sets its own course, the results can be jarring — although not necessarily threatening. The Qataris’s message to the U.S. about their strategy may follow the old Rolling Stones chorus, ‘You can’t always get what you want, but… you just might get what you need.’ Then again, the rivals of the beneficiaries of Qatar’s largesse in the region would change that last part to read ‘you just might get what we need.’

Tony Karon is a senior editor at TIME, where he has covered international conflicts in the Middle East, Asia, and the Balkans since 1997. A native of South Africa, he now resides with his family in Brooklyn, New York.